For the first time exact analytical solutions to the eikonal equations in (1+ 1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit analytical expression for the self-focusing position, where the intensity tends to infinity, is found. Based on an approximated Lie symmetry group, solution...

The energy change per electron in a chemical or physical transformation, ΔE/n, may be expressed as Δχ̅ + Δ(VNN + ω)/n, where Δχ̅ is the average electron binding energy, a generalized electronegativity, ΔVNN is the change in nuclear repulsions, and Δω is the change in multielectron interactions in the process considered. The last term can be obtained by the difference from experimental or theoreti...

The refractive index (RI) dictates interaction between light and nanoparticles and therefore is important to health, environmental, and materials sciences. Using nanoparticle tracking analysis, we have determined the RI of heterogeneous particles <500 nm in suspension. We demonstrate feasibility of distinguishing silica and polystyrene beads based on their RI. The hitherto unknown RI of extrace...

We present terahertz images of 10 μm thick histopathologic sections obtained in reflection geometry with a time-domain spectrometer, and demonstrate improved contrast for sections measured in paraffin with water. Automated segmentation is applied to the complex refractive index data to generate clustered terahertz images distinguishing cancer from healthy tissues. The degree of classification o...

The vertex-distinguishing index χs(G) of a graph G is the minimum number of colours required to properly colour the edges of G in such a way that any two vertices are incident with different sets of colours. We consider this parameter for some regular graphs. Moreover, we prove that for any graph, the value of this invariant is not changed if the colouring above is, in addition, required to be ...

The Informedia Digital Video Library Project at Carnegie Mellon University [1] combines speech, image and natural language understanding to automatically transcribe, segment and index video for intelligent search and image retrieval. Since 1995, thousands hours of video (over two terabytes of data) have been collected, with automatically generated metadata and indices for retrieving videos from...

As judged by the American College of Radiology Appropriateness Criteria, renal Doppler ultrasonography is the most appropriate imaging test in the evaluation of AKI and has the highest level of recommendation. Unfortunately, nephrologists are rarely specifically trained in ultrasonography technique and interpretation, and important clinical information obtained from renal ultrasonography may no...

To select optimal cut-off values of tumor markers in cerebrospinal fluid for the diagnosis of meningeal carcinomatosis, the concentrations of CEA, CA125, CA153, CA199, CA724, CYFRA21-1, AFP and NSE were determined by means of double-antibody sandwich enzyme-linked immunosorbent assay (ELISA) in 21 MC patients, 25 cancer patients without leptomeningeal disease (group one) and 45 meningitis patie...